Equivalences of Batch-Service Queues and Multi-Server Queues and Their Complete Simple Solutions in Terms of Roots |
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Authors: | Nam K Kim Mohan L Chaudhry |
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Institution: | 1. Department of Industrial Engineering , Chonnam National University , Gwangju, Korea freedom@chonnam.ac.kr;3. Department of Mathematics and Computer Science , Royal Military College of Canada, STN Forces , Kingston, Ontario, Canada |
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Abstract: | Abstract In this article, we first present a unified discussion of several equivalence relationships among (as well as between) batch-service queues and multi-server queues, in terms of the stationary queue-length and waiting-time distributions. Then, we present a complete and simple solution for the queue-length and waiting-time distributions of the discrete-time multi-server deterministic-service Geo/D/b queue, in terms of roots of the so-called characteristic equation. This solution also represents the solutions for the other equivalent queues, as a result of the equivalence relationships. To aid in the applications of these results, sample numerical results are presented at the end. |
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Keywords: | Batch service Discrete-time queue Equivalence relationship Multiple servers Queue length Waiting time |
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